منابع مشابه
Generic rectangulations
A rectangulation is a tiling of a rectangle by a finite number of rectangles. The rectangulation is called generic if no four of its rectangles share a single corner. We initiate the enumeration of generic rectangulations up to combinatorial equivalence by establishing an explicit bijection between generic rectangulations and a set of permutations defined by a pattern-avoidance condition analog...
متن کاملBinary search trees and rectangulations
We revisit the classical problem of searching in a binary search tree (BST) using rotations, and present novel connections of this problem to a number of geometric and combinatorial structures. In particular, we show that the execution trace of a BST that serves a sequence of queries is in close correspondence with the flip-sequence between two rectangulations. (Rectangulations are well-studied...
متن کاملA Note on Flips in Diagonal Rectangulations
Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal with local changes involving a single edge of a rectangulation, referred to as flips, edge rotations, or edge pivoting. Such operations induce a graph on equi...
متن کاملThe Flip Diameter of Rectangulations and Convex Subdivisions
We study the configuration space of rectangulations and convex subdivisions of n points in the plane. It is shown that a sequence of O(n log n) elementary flip and rotate operations can transform any rectangulation to any other rectangulation on the same set of n points. This bound is the best possible for some point sets, while Θ(n) operations are sufficient and necessary for others. Some of o...
متن کامل3-rectangulations: an algorithm to generate box packings
3-rectangulations are spatial representatives of assemblies of boxes into a box. Algorithms to generate various classes of 3-rectangulations are developed. The method is extended to specify the generation of higher-dimensional <2-rectangulations, d > 4. 3-rectangulations I consider the following combinatorial problem: how many arrangements of boxes into a box are there subject to the proviso th...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.11.004